How good is the AVL balancing rule? That is, before we consider how
much complication it adds to BST operations, what does this balancing
rule guarantee about performance? This is a simple question only if
you're familiar with the mathematics behind computer science. For our
purposes, it suffices to state the results:

The average speed of a search in a binary tree depends on the tree's
height, so the results above are quite encouraging: an AVL tree will
never be more than about 50% taller than the corresponding optimally
balanced tree. Thus, we have a guarantee of good performance even in
the worst case, and optimal performance in the best case.

Footnotes

[1] Here log2 is the standard C base-2 logarithm
function, pow is the exponentiation function, and ceil is the
“ceiling” or “round up” function. For more information, consult a
C reference guide, such as [Kernighan 1988].